The invention relates to methods for converting time-of-flight values of ion signals into mass values in time-of-flight mass spectrometers with extreme mass accuracy. Modern time-of-flight mass spectrometers can measure the mass-to-charge ratios m/z of the ions with a precision which would have been unthinkable only a few years ago, and this not only in individual, spectacular measurements, but practically as daily routine. The precision, i.e. the reciprocal spread of measurements repeated many times, achieved today with highly developed time-of-flight mass spectrometers, using internal mass calibration, is now better than one ppm (part per million), often 100 ppb (parts per billion) or even better. According to current expert opinion, it should then also be simple for such an instrument to bring the accuracy of measuring the mass-to-charge ratios m/z, i.e. the deviation from the true mass value, to the same order of magnitude by a calibration and the use of mass reference substances which provide ion signals in the same spectrum (“internal references”). It is apparent, however, that calibration functions which should provide a very accurate mass determination by a mathematical representation, i.e. by a functional relationship between mass and time of flight, constantly pose new challenges as the demands placed on the measurement accuracy increase.
In mass ranges between 1,000 and 6,000 atomic mass units, time-of-flight mass spectrometers with ionization by matrix-assisted laser desorption (MALDI-TOF) are currently advancing toward mass resolutions of better than R=m/Δm=50,000, where Δm is the full width at half-maximum of the mass signal at mass m. These values are surprising; they mean that, in the higher mass range, the MALDI time-of-flight mass spectrometers surpass all other types of mass spectrometer, even ion cyclotron resonance mass spectrometers (ICR-MS) and electrostatic Kingdon ion traps (for example, the Orbitrap™), whose fundamentally high mass resolution decreases as 1/m or
  1      m  toward higher masses. The successes of time-of-flight mass spectrometers are based on improvements to the acceleration electronics and the detector, an increase in the sampling rate in the transient recorders and, in particular, better mastery of the MALDI processes by using improved laser technology, as described, for example, in DE 10 2004 044 196 A1 (A. Haase et al., corresponding to GB 2 421 352 B and US-2006-0071160 B1). A major contribution to the continuous improvement of this technology has been made by the long-known time-delayed acceleration, as described by U.S. Pat. No. 5,654,545 A (Holle et al., corresponding to GB 2 305 539 B), for example, and by the shaping of a temporally changing acceleration as described in DE 196 38 577 C1 (J. Franzen, corresponding to GB 2 317 495 B and U.S. Pat. No. 5,969,348 B1), which causes the region with maximum mass resolution to extend evenly over a wide mass range rather than being located at one point of the mass spectrum.
Time-of-flight mass spectrometers with orthogonal ion injection (OTOF), which are usually operated with electrospray ion sources (ESI), but are now increasingly being operated with other types of ion sources, are also advancing into these regions of mass resolution by virtue of similar technical improvements. Here the acceleration of the ions of a primary ion beam into the flight path of the mass spectrometer, at right angles to the previous direction, is carried out instantaneously by suddenly switching on the accelerating voltage.
If ions are accelerated to a kinetic energy E in an ideal way, i.e. simultaneously by switching on the acceleration in MALDI-TOF or OTOF mass spectrometers in an infinitesimally short time, it is possible to determine the relationship between their time of flight Δt=t−t0 over a distance L and their mass m from the basic equations:
                              E          =                                                    (                                  m                  /                  2                                )                            ×                              v                2                                      =                                          (                                  m                  /                  2                                )                            ×                                                L                  2                                /                                                      (                                          t                      -                                              t                        0                                                              )                                    2                                                                    ;                            [        1        ]                                          m          =                      2            ⁢                                                  ⁢            E            ×                                                            (                                      t                    -                                          t                      0                                                        )                                2                            /                              L                2                                                    ;                            [        2        ]                                t        =                              t            0                    +                      L            ×                                                            m                                      2                    ⁢                                                                                  ⁢                    E                                                              .                                                          [        3        ]            But for various reasons, these equations only constitute approximations.
For instance, it has long been known that, in MALDI mass spectrometers, the ions of all masses receive a common velocity distribution with a common average initial velocity v0, in the adiabatically expanding plasma of the matrix-assisted laser desorption (MALDI). The kinetic energy E after the electric post-acceleration of the ions thus comprises two components: the energy EU caused by the electric acceleration, and the initial energy E0=(m/2)×v02, which originates from the MALDI process:E=EU+E0=EU+(m/2)×v02.  [4]
If one introduces this additional condition into the above Equations [2] and [3] and then makes several approximations which are based on the fact that the initial energy E0 is very small compared to the energy EU from the electric acceleration, one obtains a very good approximate equation for the time of flight as a function of the mass:t≈c0(√{square root over (m)})0+c1(√{square root over (m)})1+c3(√{square root over (m)})3,  [5]and also a very good approximate equation for the mass as a function of the time of flight:m≈k2(t−t0)2+k4(t−t0)4,  [6]which can be used to a large extent for both MALDI time-of-flight mass spectrometers and time-of-flight mass spectrometers with orthogonal injection (OTOF-MS).
The coefficients c0 to c3 and t0, k2 and k4 are determined by mathematical fittings from the ion signals of a mass spectrum of a calibration substance with accurately known masses. Such fitting procedures are known to those skilled in the art. For an OTOF-MS, where the ions have no initial velocity, the coefficient c3 can also be assumed to be zero. The physical meaning and origin of the coefficients are immaterial for the application, but they are given below for the sake of completeness:
                                                        c              0                        =                          t              0                                ;                ⁢                                  ⁢                                            c              1                        ≈                          L                                                2                  ⁢                                                                          ⁢                                      E                    U                                                                                ;                ⁢                                  ⁢                                            c              3                        ≈                                          L                ·                                  v                  0                  2                                                                              32                  ⁢                                                            (                                                                        E                          U                                                                    )                                        3                                                                                ;                ⁢                                  ⁢                                            k              2                        =                                          2                ⁢                                                                  ⁢                                                      E                    U                                    /                                      L                    2                                                              +                                                m                  0                                ⁢                                                      v                    0                    2                                    /                                      L                    2                                                                                ;                ⁢                                  ⁢                              k            4                    =                      2            ⁢                                                  ⁢                          E              U                        ⁢                                          v                0                2                            /                                                L                  4                                .                                                                        [        7        ]            
It is, however, impossible to instantaneously, i.e. in no time, switch on an accelerating field by applying a voltage to a diaphragm which is arranged in a stack of other diaphragms and which has a considerable capacitance with respect to the others. If the diaphragm has a low-resistance connection to a power supply then, after the capacitance has charged up, which takes a finite time, the inductance of the supply lead means there is always a periodic overshooting, which is only slowly damped by the ever-present resistances of the materials. This overshooting has very damaging impacts on the acceleration of the ions and hence on the calibration function. Where possible, the overshooting is therefore damped by additional resistors in the supply lead to such an extent that the limiting aperiodic case of the switching occurs, which results in a constant voltage in the shortest time, but not without a transition curve. In fact, a slightly larger resistor is used to enable better reproducibility of manufacture, which means that the approach remains somewhat removed from this actually ideal aperiodic limiting case, and therefore an approach to the final strength of the acceleration field takes the form of a creeping exponential curve. This “dynamic acceleration” changes the calibration function for both OTOF-MS as well as for MALDI-TOF-MS.
In DE 10 2007 027 143 B3 (A. Brekenfeld) a method is now disclosed for taking account of this dynamic acceleration in the calibration function by assuming a reduced mass m−m0. The formal assumption of a reduced mass m−m0 is based simply on the observation that the systematic mass deviations become relatively larger toward smaller masses. Since the light ions leave the acceleration region before the full accelerating voltage is reached, they do not possess the full acceleration energy EU. Mathematically, it is scarcely possible to take account of the energy defect, while assuming an analogous mass defect leads to simple solutions for the calibration function.
If one introduces the reduced mass m−m0 into Equation [5] and expands it with respect to √{square root over (m)}, one obtains a further term c−1×(√{square root over (m)})−1, so that the series expansion is now:t≈c−1×(√{square root over (m)})−1+c0×(√{square root over (m)})0+c1×(√{square root over (m)})1+c3×(√{square root over (m)})3  [8]The reduction mass m0 is obtained from the coefficients of 2c−1/c1. Introducing a reduction mass m0 is therefore equivalent to introducing the term with
      1          m        .
Similarly, introducing the reduced mass m−m0 into Equation [6] leads additionally to a constant term:m≈k0+k2(t−t0)2+k4(t−t0)4, where k0=m0.  [9]
The two Equations [8] and [9] have only four coefficients each. Further terms can, of course, be added to both equations, for example with the coefficients C−2, c2, c4, k1 and k3, to improve the accuracy of fitting. For best results, the additional terms should be selected experimentally. The additional terms do not have a physical interpretation.
The calibration functions on the basis of Equation [8] or [9] provide good results. With only one added term, i.e. with 5 coefficients each, the systematic residual errors over an extremely wide mass range of between 120 up to over 3,000 atomic mass units can be reduced to one to two parts per million of the mass. With this calibration function it is particularly possible to successfully extrapolate to large masses far beyond the calibrated range.
In time-of-flight mass spectrometers, the ion currents of the ions reaching the detector are amplified, digitized with a constant digitizing rate and stored as digital values in the order they were measured. Normal practice is to acquire several hundred to several thousand individual spectra in succession from one sample and to add them together, digital value by digital value, to form a sum spectrum. The original sum mass spectrum therefore consists of a long series of digital measured values where the associated times of flight t of the ion currents do not appear explicitly but merely form the indices of the measurement series. The measurement series is analyzed for the occurrence of prominent current signals; these represent the ion signals. A large number of algorithms and software programs, which are commonly called “peak recognition programs”, are available to identify these ion signals. The time of flight t for an ion peak, whose measured values regularly extend over several indices, is interpolated from the indices of the measured values. By using good peak recognition procedures, it is possible to obtain precisions for the times of flight which are much better than the time intervals of the digitizing rate.
The precision of the time-of-flight determination depends on the digitizing rate. The transient recorders of modern commercial time-of-flight mass spectrometers usually use a digitizing rate of two to four gigasamples per second; however, it is to be expected that, in the future, scanning rates of eight or more gigasamples per second will be available and will be used. It is therefore to be expected that with good interpolations of the peak recognition procedures, it will be possible to achieve precisions of approximately a hundredth of a nanosecond for the time-of-flight determination. A very precise peak recognition procedure, which is based on the simultaneous consideration of all ion signals of a group of isotopes, is described in DE 198 03 309 C1 (C. Koester, corresponding to U.S. Pat. No. 6,188,064 B1 and GB 2 333 893 B). Since a mass range of up to some 6,000 atomic mass units is scanned in approximately 100 microseconds, mass accuracies much better than one part per million are to be expected in principle. As has already been mentioned above, the precision of highly developed time-of-flight mass spectrometers is currently around 100 ppb, i.e. one ten millionth of the mass-to-charge ratio m/z.
As the development of time-of-flight mass spectrometers progresses toward ever increasing mass accuracies, one encounters phenomena which cannot yet be explained. Although highly developed time-of-flight mass spectrometers display precisions which are around ±100 ppb, the true mass values show erratic deviations of several hundred ppb up to a few ppm despite being referenced to one or more internal reference masses. These deviations differ from instrument to instrument and even from substance to substance in the same instrument. These individual, apparently nonsystematic mass deviations for ions of individual substances cannot be removed by a calibration with one of the calibration functions mentioned above despite the high precision of the measurements.